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Question: Answered & Verified by Expert
If the line $y=m x+c$ be a tangent to the circle $x^2+y^2=a^2$, then the point of contact is
MathematicsCircleJEE Main
Options:
  • A $\left(\frac{-a^2}{c}, a^2\right)$
  • B $\left(\frac{a^2}{c}, \frac{-a^2 m}{c}\right)$
  • C $\left(\frac{-a^2 m}{c}, \frac{a^2}{c}\right)$
  • D $\left(\frac{-a^2 c}{m}, \frac{a^2}{m}\right)$
Solution:
2325 Upvotes Verified Answer
The correct answer is: $\left(\frac{-a^2 m}{c}, \frac{a^2}{c}\right)$
Find points of intersection by simultaneously solving for $x$ and $y$ from $y=m x+c$ and $x^2+y^2=a^2$ which comes out as $\left(-\frac{a^2 m}{c}, \frac{a^2}{c}\right)$.

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